{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fisher's Linear Discriminant\n",
    "\n",
    "Contrary to the least squares' approach in solving the classfication problem, the _projection_ way of solving the problem is by reducing the dimension of the input vector vector ${\\bf x} \\in \\mathbb{R}^n$ onto $\\mathbb{R}$ via the weight vector ${\\bf w} \\in \\mathbb{R}^n$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A first approach to project and classify\n",
    "In its simplest form,\n",
    "> we look for ${\\bf w}$ such that the separation of the projected class means is as large as possible.\n",
    "\n",
    "Denoting for a class $C_k$, its mean vector by\n",
    "\n",
    "$$\n",
    "    {\\bf m}_k = \\frac{1}{N_k}\\sum_{n \\in C_k} x_n\n",
    "$$\n",
    "\n",
    "In order to maximize the separation between classes, we consider the following optimization problem\n",
    "$$\n",
    "\\begin{align}\n",
    "    \\text{max } \\quad & {\\bf w}^T ({\\bf m}_2 - {\\bf m}_1) \\\\\n",
    "    \\text{s.t. } \\quad & {\\bf w}^T{\\bf w} = 1\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from numpy.random import seed, multivariate_normal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%config InlineBackend.figure_format = \"retina\"\n",
    "plt.rcParams[\"figure.figsize\"]  = (12, 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to understand the result that the optimization problem above yields, we will consider two classes coming from a multivariate normal each with parameters as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "cov1 = np.array([\n",
    "    [1, 0.8],\n",
    "    [0.8, 1]\n",
    "])\n",
    "mu1 = (3, 6)\n",
    "\n",
    "cov2 = np.array([\n",
    "    [1, 0.5],\n",
    "    [0.5, 1]\n",
    "])\n",
    "mu2 = (3, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we sample 100 observation from each distribution and compute the class mean."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "seed(314)\n",
    "# The training dataset\n",
    "X1 = multivariate_normal(mu1, cov1, 100)\n",
    "X2 = multivariate_normal(mu2, cov2, 100)\n",
    "# The mean vectors\n",
    "m1 = X1.mean(axis=0)\n",
    "m2 = X2.mean(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 304,
       "width": 699
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(*X1.T, alpha=0.6, c=\"tab:red\")\n",
    "plt.scatter(*X2.T, alpha=0.6, c=\"tab:gray\")\n",
    "plt.scatter(*m1, marker=\"^\", s=200, c=\"tab:blue\")\n",
    "plt.scatter(*m2, marker=\"^\", s=200, c=\"tab:blue\")\n",
    "plt.grid(alpha=0.7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the optimization problem above, the weight vector ${\\bf w}$ that maximizes the separation of mean classes subject to a unit norm vector is given by\n",
    "\n",
    "$$\n",
    "    {\\bf w}^* = \\frac{-2 ({\\bf m}_2 - {\\bf m}_1)}{\\left[({\\bf m}_2 - {\\bf m}_1)^T({\\bf m}_2 - {\\bf m}_1)\\right]^{1/2}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 1)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "what = -2 * (m2 - m1) / np.sqrt((m2 - m1).T @ (m2 - m1))\n",
    "what = what[:, np.newaxis]\n",
    "what.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 304,
       "width": 715
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(X1 @ what, color=\"tab:red\")\n",
    "plt.hist(X2 @ what, color=\"tab:gray\")\n",
    "plt.grid(alpha=0.7);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "slope = what[1] / what[0]\n",
    "projected_space = np.linspace(-0.5, 1.3, 100)\n",
    "c = 15 # coefficient to \"shift\" the projected line\n",
    "projected_line = projected_space * slope + c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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CsJBYv37dr7K+e1dusahoOi3FYjLVqpxsVs79+6reuaPUa69q7MKFfg+3Lwi+0SmsbAB8BLsdUigU9Cu/8is7Ls9ms30YDQAAAIBBEZs6SpAbcNVMRoXLV1S5dVN2+rBGT516qnowdvy4armcKrduqnD5iuxUauiCJoJvdBorGwCC3Y6ZmZlpePni4qKMMbIsq8cjAgAAAAD0QumNq3Lu3ZWdPtyw36dl24rPzsqR5Ny7q9LVN4cqbBrk4JuK+v5iZQOGHcFuhxw+fFiJRELVavWpy9fX17WysqJUKtWnkQEAAAAAuqX2cMlvLbBS1Oj5U3seG5ueVvnGDVVv31bt4dLQBE+DGHzTViJYWNmAYRXp9wAGhWVZe1btAgAAAAAGj7OQkZsvKJpOP1WF2ohl27JTKbn5vJyFTI9G2F9bg+/Y9PSex8amp+WuFDeD76Bav35dj3/zt7T6ta+p/M435K2vy3ievPV1ld/5hlbf+Joe/+Zvaf369X4PFcCAo2K3g2ZnZ7WwsLDj8mw2qxdeeKEPIwIAAAAAdJOpVmVcV4rFmjreisdlXFdm22rPsGu0FF6Sin/4B6p+644s25ZxHFmjo7tex/bgO4gVmIPcVgJA+BDsdhAVuwAAAAAwXKxEwg8tmwxqjeMokkzKSiS6PLLeaNSSwFSr8tbWJEvyqo7qjx5JkrxKRfbEhGIzM7InJhpeX9CD70FsKwEgvAh2O2i2wUld8it2AQAAAACdFYQNk+Kn52SnU3KyWcWOH9+zHYNxXbmFguLHjm1WtIbZ+vXrKly+IufuXbnFoqLptLxyWbUHD+SVSpKeBLXGyJLk5vPySiV5xaLic3OKHjmy4zqDHHzTTxlA0BDsdtBuFbsEuwAAAADQOUHauCo2dVSJM/Ny7t9XLZdrWMW5oZbLyZ6cUGJ+PvRBX6OWBN76muo3b8nU64pMTMiSX6VrGSNjjKKHD8tUKqoXClImIysef6pyN+jBdzv9lMP+fAMIJoLdDtqtYpdWDAAAAADQGY2qRBWLyVSrcrJZOffvq3rnjlKvvaqxCxd6MqbxSxdVvXNHlVs35civ1twa/BnXVS2Xk5tf1sjZcxq/+EpHb78flcuNWhLUsotySyVFEglFkkn/QMuSu7oqSTKVyublbqmk2oMHTwW7QQ++6acMIGgIdjuIHrsAAAAA0D1B3bgqMTen1Guv+oHzvbsq37ghO5Xygz3HkVsoyJ6c0MjZc0q99mrHxtSvyuVGLQm8cllesSjjOLKfeWbzWGt0VNbamiTJLZf9y0ZG5BUK8lZW5JXLsuLxrgbfnTLs/ZQBBA/BbgfRYxcAAAAAuifIG1eNXbggO5VS6eqbqt5+bzNojSSTih87psT8vMYvvtKx8fSzcrlRSwJvtSivWlUkkZAsa/NYKxKRNToqeZ4i0aiM68rL52WMUX1lRZX33pM8ryvBd6cNcz9lAMFEsNtBzz33XMPLc7mcXNeVvU8PHgAAAABAY2HYuCoxN6fE3FzXWyP0u3K5UUsC43rSk166XrksGSNZlqxYTFYkItm2YrOzMvW6vJUV1VdWJEmReFyJM2c6Hnx3w7D2UwYQXAS7HZRMJjU5OamVJx9QG1zX1dLS0q7BLwAAAABgb2HauCo2dbSrt9nvyuVGLQlMpSJvbU2mVpMikQ+D3UhExhhFxsYUGR9XbGpKXrms6nvvyYrHNfGpf6yJT/9YaMLPfvdTBoCtIv0ewKBhAzUAAAAA6Dw2rvJtrVyOTU/veWxselruSnGzcrlTNloS1PN5GddV/dEj1XI5GceRcRzJ8/wDPU9epSJTqciUyzL1uqQnz43nKXHmTKhCXenDfsojZ8/JVCt+ZfjCgpxsVtWFBZVv3JCpVgLfVgLAYKBit8NmZmb07rvv7rg8m83q5Zdf7sOIAAAAACD82LjKF4TK5a0tCaoLGXnLebmrq7JiMb+/rmXJin4YNxjXlanXVc9mZU8ckltcDXWbgl73UwaA3RDsdhgVuwAAAADQeWxc5QtK5fJGS4K1v/gLeeWyrNFRRcbH5RYK8hxHxhhZkoznKZJIyEokVF9dlbl5S5Gx0dC3KehVP2UA2AvBbofNzMw0vDybzfZ4JAAAAMDwIFwZfGxc5QtK5XJibk7jn/iE1v/mb2SKRcmy5BkjxWKyajWZWk1GkqLRzUper1iUJWnkhRcGpk1Bt/spA8BeCHY7jIpdAAAAoHeqmYxKb1z1e44+WQ5t2bbsdEqJM/Nyn/+I7MnJfg8THcLGVcGqXLbHk4pNTfkbpT0Jmy3blolGP+ynG436Y7Qs2YcOyU6lNP4DP6CxCxc6Ph4AGDYEux1GxS4AAADQG+vXr6tw+Yqcu3flFouKptNSLCZTrcrJZuXcv69KrabE/Jk9r4dq3/DY2LiqcPmKnHt3Vb5xQ3Yq5bcbcBy5hYLsyYmB3rgqSJXLplqVNTKi2IkTih4+LLdY9DdOi0RkT0xI0lOXuWtrskdHFX3mcMfHAgDDiGC3w3YLdqnYBQAAQCOEigdTzWRUuHxFlVs3ZacPa/TUqacqF2PHj6uWy6meX5Zuf0vV06d3hHz7VfuOX7o4kMFg2LFxVXAql7e2hYiMjioyOrrjmK2XeQsLsmx74Da0G2Z8hgH9RbDbYbu1YqBiFwAAAFsRKran9MZVOffuyk4fblixaNm24rOzshIjcleLKl1986nHs5lq3+qdO0q99ipLxgNo2DeuCkrlcpDaQqC3+AwDgoFgt8Ompqb0+c9/XrOzs5qZmdn8uVslLwAAAIYPoWJ7ag+X/DBhpajR86f2PNZOjqn+6JGqt2+r9nBJsamjTVf7Vm7dVOHyFdmpFAFFQA3zxlVBqFwOUlsI9E4vP8OGdfIGaBbBbofFYjF9+ctf7vcwAAAAEFCEiu1zFjJy8wVF0+k9KwQlSVZEViIh9/77chYyik0dbbra15Hk3Lu7o9o3yAhBhksQKpeD0hYCvdGrzzAqgoHmEOwCAAAAPTTIoWKvmGpVxnWlWKy5fxCxZVxXplptqdo3Nj2t8o0bT1X7BhUhyHDrZ+VyUNpCoDd68RnGqhageQS7AAAAQI8MaqjYa1s3bGqK525u2NRKta9l27JTKbn5/Ga1bxARgqDfgtAWAt3Xi88wVrUArSHYBQAAAHpkEEPFfmhlwyYZT6ZalZ1OK356TtVbN1uq9rXi8c1q3yAiBEFQBKEtBLqrF59hrGoBWkOwCwAAAPRIqy0Egh4q9ksrGza5a+uy4nEl5mcUmzoqZyHTUrWvcRxFkklZiUSnht9RhCAImmHe0G7QdfszjFUtQOsi/R4AAAAAMCw2WgioVmvqeOM4my0E8LTxSxcVP3FSbn5ZTjbrhw1bGNf1L69WZB+a2NywaaPat57P7/g32xnX9fuDPqn2lfzgYe3aNZXefFNr166p9nCpO3ewCVtDkNj09J7Hxqan5a4UN0MQAGhVtz/D2qkIBoYVFbsAAABAj7TSQmAjVIwfO7YZKuJDzW7YFE0fVmL+zGaVaivVvrVcTvbkhBLz8/LWSnr8W38QqM3JaO0BtG6jVUQtn5eiUdWOTvF+aFK3P8NY1QK0jmAXAAAA6JGDhoqEDo01s2FT4SPzsicnn/p345cuqnrnjiq3bsqRX826NaAwrqtaLic3v6yRs+cUffZZPf7N3wrc5mTDFoLQuxXtqGYyKr1xdXNypvL881LE0gdf+1rfJmfCptufYa1ujBn0VjlALxDsdpExRsViUYuLi8pms3rw4IF+7ud+TpZl9XtoAAAgwAgvBluroeJGCwE0tt+GTYtvv93w3zRT7Tty9pySH/+41v7yLwO5OdmwhCDbA7kgVEsjXNavX/ff71smZ4wxUs1V+Z1v9G1yJoy6+RnGqhagdQS7XXL+/HllMhmtra09dflnPvMZpVKpPo0KAAAEGeHFcGglVEy99irPeZNa3bCpmWrf8YuvBHpzsmEIQRoFckGolt4Qpom4MI21k6qZjAqXr+yYnLHHxyVJo+fP921yJoy6+RnGqhagdQS7XVIqlXaEupK0uLhIsAsAAHYIeniBzmo2VCRc6K79qn2DvkP7oIcguwVyG/pZLR2mibgwjbUbgjw5E1bd/AxjVQvQGoLdLpmZmdHCwsKOy7PZrF544YU+jAgAAARVkMMLdM9+oSJ6Z7dq3zBsTjbIIUhQA7kwTcSFaazdEPTJmTDr1mcYq1qA1hDsdsnsLrPli4uLPR4JAAAIuqCGF+iNVlsIoHfCsDlZUEOQdsOeoAZyYZqIC9NYuyUMkzNh143PMFa1AM0j2O2SmZmZhpdns9kejwQAAARZUMMLAOHZnCxIIUinlv23G8h1qxI+TBNxYRprt4RhcmY7VnH4WNUCNIdgt0uo2AUAAM2gmggIrjBtThaEEKSTy/4PGsg5d++q8o13u9JPNkwTcWEaazeFZXJGohfybljVAuyNYLdLqNgFAADNCGM1ETAswrg5Wb9CkE4v+z9IIGfqda2+/rq89XJX+smGaSIuTGPtprBMzgx7L2QAB0ew2yVU7AIAgGaEqZoIGEaDvDlZJ3V62X+rgVx9aUkyRlappOjRo13pJxumibgwjbWbwjA5Qy9kAO2I9HsAg4qKXQAA0IyN8KKez/tfwvewUU1kp9N9WeoNDKONzclGzp6TqVb8JesLC3KyWVUXFlS+cUOmWhnqHdq3LvuPTU/veWxselruSnFz2f+uxz0J5OzJCdVyub1vP5eTceuS5yl69Kjis7M7guCNYNlOH94Mllu1MRGnWq2p443jyLLtvkzEhWms3TZ+6aLiJ07KzS/LyWZ3fNYa15WTzcrNLyt+4mTPJ2e2T4p047ULYHAR7HbJbsFuLpeTu8+XNgAAMDxaDS+CsNQbGDZjFy7omc99Voc+8cMaffGjspNJWZGI7GRSoy++qEOf+GE987nP7rtEuvZwSWvXrqn05ptau3Ztz2AzTNpZ9r+XZgO5+tJDWRFbsu2OBcuNhGkiLkxj7bbdJmfcUklucaWvkzPdmBQBMFxoxdAlyWRSk5OTWllZeepy13W1tLSk5557rk8jAwAAQcNSbyD42tmcbNA3RerWsv+NQK5w+Yqce3dVvnFDdirl/3vH8cPIyQnFpqblra3JisW62k82DMv6N4RprL0wduGC7FRKpatvqnr7Pbn5gizLkmIxjb74ohLz8xq/+ErP34f0QgbQLoLdLpqdnd0R7Ep+n12CXQAAsKHZ8GKYl3oDQdHq5mTDsClSN3uFNwrkjOsqkkwqfuyYEvPziiTHtPr6n8l4XnPjbaOfbJgm4sI01l7YPjnzQT4vRaN69mf/Sd9CUnohA2gXwW4XzczM6N13391xeTab1csvv9yHEQEAgKBqJrzoRzURgIMblk2RWt3ozC0UFD92rOll//tVS69du9azTSjDNBEXprH20sbkTOzttzf/f7+wgSqAdhHsdtHsLstdFhcXezwSAAAQBu0s9QbQe/u9V7dvirTdxqZIjrS5KVIYw7VeLfvfrVq628HydmGaiAvTWIdRr1+7AAYPwW4X7baBWjab7fFIAABAmLS61BtAbzXTMzeSHN/cFGn0/Kk9ry82Pe1v6PRkU6Qwvv/7uey/H/1kwzQRF6axtiOM949eyADaRbDbRVTsAgAAAIOl2Z65iXNnh2pTpH4v++9XsBymibgwjbUVYd+ckF7IANpBsNtFVOwCAAAAg6OVnrm1XM6vHBwZaeq6B2FTpH4u++93sIz+GITNCXntAmgHwW4X7RbsUrELAAAAhE8rPXPrHyxJrqfoM880dd2DsilSP5f90092uAzS5oS8dgEcFMFuF+3WioGKXQAAACBcag+XWuqZW1tclFxX9Q8+GMpNkfq17H9Y+sli8DYn5LUL4CAIdrtoampKlmXJGPPU5cvLy6pUKhppclkWAAAAgP5yFjIt9cyNHjki9/FjWdEomyL1waD2k4Wv1YmWMG1OyGsXQCsi/R7AIIvFYpqammr4O9oxAAAAAOFhqlUZ15VisaaOt+Jx2em07CNH5OaX5WSz/r/fep2uKyeblZtfVvzESTZFAprU6kTL1s0JAWCQULHbZTMzM8rlcpKkZDKp2dlZzczMqFar9XlkAAAAAJplJRKybLvpzc2M48jrhfv4AAAgAElEQVQ+dEjJ7/8+VW7eYlMkoIMOMtES9s0JAaARgt0u++3f/m3F43HNzs7q0KFDsiyr30MCAAAANtHPsTnx03Oy0yk52WxLPXMP/aNPKvn938+mSEAHHWSiZRA2JwSA7Qh2u+xjH/tYv4cAAAAQKASJwVDNZFR646rfp/JJ2GjZtux0Sokz8xq/dJGwcYvY1FElzszLuX//AD1zj7IpEtBBB51oGZTNCQFgA8EuAABAAAxD4EOQGBzr16+rcPmKnLt35RaLiqbTUiwmU63KyWbl3L+v6p07Sr32qsYuXOj3cANj/NJFVe/cUeXWTTnyN2XaGigZ11Utl5ObX9bI2XM7euayKRLQGe1NtADA4CDYBQAA6KNhCTsJEoOjmsmocPmKKrduyk4f1uipU0+Fk7Hjx1XL5VS5dVOFy1dkp1ID8RrshMTcnFKvveq/lumZiy4ahsm+drU70QIAg4BgFwAAoE+GJewcxCAxzKFL6Y2rcu7dlZ0+3LDKzbJtxWdn5Uhy7t1V6eqbgX8+eqX2cEnGcTT6sfOyYjG5KwWZSpWeueiYYZns6wQmWgCAYBcAAKAvBjHs3M0gBYlhD11qD5f8sa8UNXr+1J7HxqanVb5xQ9Xbt1V7uBSa4LobdnverZERRaeOauSFFxQ/eTJUAf9WYZ6o6KR+Pw7DMtnXSWMXLshOpdicEMDQItgFAKAP+v3lEf03SGHnXgYpSByE0MVZyMjNFxRNp/fcbEjyX4N2KiU3n5ezkAnc89Erez3v9WxW9uSETK0eyv6dYZ+o6JQgPA7DNNnXaYm5OTYnBDC0CHYBAOihIHx5RP8NUti5n0EJEgcldDFVv22AYrGmjrficRnXlalWuzyyYBqU572RQZio6ISgPA7DMtnXTWxOCGAYEewCANAjQfnyiP4blLCzGUEPEput8BqU0MVKJGTZdtOPr3EcRZJJWYlEl0cWTIPyvG83yIF1K3r9OOx2vhmmyT4AQGcR7PbAN7/5Td2+fVvZbFaLi4ubP7/4xS/qe7/3e/s9PABAD/AlGlsFPezspKAGia1Uzw9S6BI/PSc7nZKTzSp2/PieEwvGdeUWCoofO6b46eE7Hw3S877doAbWrerV47Df+cZOp4dmsg8A0FkdDXYty/pBSf9U0vdJOixpWdLbkr5kjPmjTt5WmHzxi1/U7/7u7+64/Kd/+qcJdgFgSPAlGlsFNezshiAGia1Wzw9ShXVs6qgSZ+bl3L+vWi7X8Hy0oZbLyZ6caKt37IOVsr7y9QV9/odO67nJ0YMOuy8G6XnfapAD61a0/Dhcv661f//vFH3msKJTU033b23mfGPFE/JKJUUOHWpq7GGe7AMAdFbHgl3Lsv6ZpH8u6ZGkP5D0QNIRSd8p6aKkoQ12Z2ZmGl6+uLjY45EAAPqBL9HYLohhZ7f0Okjcz0Gq5wetwnr80kVV79xR5dZNOfLPO1sfA+O6quVycvPLGjl7TuMXXznwbf13X/2GXr/5UPfz6/rKz39XB0bfO4P2vG8Y1MC6Vc0+Du5qUbXsotxiUe7KityVoqLPPNNUb/xmzze19+/LVB1FjZH2OEduCPNkHwCgszoS7FqW9VPyQ93XJf3HxpjVbb9v7q+hATW7y4dzNpvt8UgAAP3Al2hsF7Sws9t6GSTu5yDV8yMvnBuoCuvE3JxSr73qVxHeu6vyjRuyUyk/mHQcuYWC7MkJjZw9p9Rrrx549cA72RW9fvOhJOlP332od7IrenF2spN3pasGtbJ+UAPrVjXzONQfPZKTycgtleStr/uPRb0ub329qd74zZ5vvGpVtYWMag8eKPGRjwz0ZB8AoLMi7V6BZVkRSb8maV3Sf7I91JUkY0yt3dsJMyp2AWC48SUajYxfuqj4iZNy88tysln/NbKFcV052azc/LLiJ052Nezsto0gceTsOZlqxa9KX1iQk82qurCg8o0bMtVK20HifrZWz8emp/c8NjY9LXelqOrt24ocmpCdTqmez+94nrbbCF3sdDrQocvYhQt65nOf1aFP/LBGX/yo7GRSViQiO5nU6Isv6tAnfljPfO6zbW3k+KXXbz/1/3/9z27vcmQwbVTWD9LzLn0YWKvW3Fc04ziybDvwgXWr9nsc3NWinExG9UJBlm0rkkwqMjam6NGjip86pdHz52UlRjar+6uZzFP/vpXzTeLkScmKSMbIuXt3z2MHYbIPANA5najY/T5JpyVdlpS3LOvTkl6UVJH0V8aYv+zAbYQaFbsAMNwGteoL7elV1WRQjF24IDuVUunqm6refm9zA6FIMqn4sWNKzM9r/OIrXb2fB62e91aLA1lhnZibU2JuTrWHS3IWMjLVqqxEouneoXvZWq27IWxVu4NaWT9MrWD2st/jUMsuyi2VFEkkZI2OysvnZY+Py56YkLR/b/xWzzfR6Wm5jx6pvrQkK5Ho68oGAEB4WMaY9q7Asr4g6V9K+g1JPyTppW2HfF3Sa8aYD/a5nrd2+dXZ+fn5sStXrrQ1zn66e/euPvOZz+y4/OjRo3r99df7MCIg/B49eiRJOnLkSJ9HAuzPW19X+W//VvXHjxU9csSvytmN8VR/9EjRZ57R6Hd+pyJjY70baMiF9bzgrqyo9n5WbiEvr1qVPCNFLEUSCdmptGLHZmVPhiMIa5a3vi63WJTqdSkalT0x0ZPXeu3991W59U0ZY2SPj+97vFsqybIsjZx9XpFDh1R55xuq55dlJUZkJ8eefi8bT+7auky1omj6sEZe/Gjgn7duPg+v33yoe8vrOy4/cXhMP3Juquvj2nodec+TFY/r2X2qJhtxV1YG7nmXpMo3viHn/n3Jju75XnBLJcmtK378hEY++kIPR9gbuz0Opl6X+/iRvEpFkZFRmXpNxvPPG3Y6/fSV7PK5vf18Y+p1GceRjJEsS1Y8Liv6YZ2VWypJNcdf3eO6fqV0IiFFbMnzV/FY8bjsQxNKzJ9R9GiwJxDCIKx/NwDonl6dF37mZ35GN2/evG6Mebnd6+pExe7GJ8p/KWlB0o9I+g+STkr6XyR9UtLvyd9AbSg9++yzDS9//PixXNeVvc8MLgAg3CJjY37l3+qq3LX1vb9Er/k9/OxUmlB3SNiTk7InJ/sWdvZDZGysP/ctGpUillTbe1n9Ju9JC5VoVPbkpBLzZ6Tb35K7WlT90aOGoUs0fViJ+TOBDvf8yYT35RYKDSYTUoodO9bW+B+Xqg1DXUm6t7yux6WqnhnfuSKhE+NqdB3ukWdk2bYqjx+3fN8G6XnfKnbsmNzCiur5ZbnSvoF17Nj+G3qF0W6Pg6k5fvuNiO2Huq6rSCKhSDK580qsiKxEQl61KrdY/PDctnG+KVfl5pflOY7kupKRZEmybUXicUWS47LicclzZY2MKH7ipEy1+vRkXyzmh8oDOtkHADi4TgS7G6mkJb8y9++f/P9vWJb1k5Lek/SKZVkf36stw24ptWVZb0Wj0QsvvbS9EDhcJicntbKy8tRlrutqampKzz33XJ9GBYTX22+/LUkK+7kBw6OaTOrxjbc3d8beb4nlM6+Gf+l9r3FewH5qR6f0wde+pvI73/D7Y+6zBL1844ZGX3xRz/7sP9lcXl89ffrDdhL335dxXb9tQzqtxPxM19tJtGv9+nUV/uiP5dy9K7dYVDSd9sPrWk31fF725ITiJ07uuhlUMz73f/yNXv/27o9taUz6ys8//T7txLh2u473z/m9nZ+9efPA9y3sz3sj62NjfiuYb3xD7kqxYSuY+ImTSn3yk231Wg66Ro+DVyqpls3K1Ov+5Oz4uOJzc4rW6jv+vVcub/bXnRgZ0eT5jyk2dVS1o1N68Hu/p/Lf/b2sWEymXverdCMRGc/zK3KfBLaxkydVW1x86nzTjRYpeBp/NwDYrlfnhdHR0Y5dVyeC3fyTn5ktoa4kyRhTtizr/5P0WUn/UNLQ9tudnZ3dEexKfp9dgl0AGHzD1k8VCKJO9EztZl/abqtmMipcvrI5wTR66tRT4Xbs+HHVcrnNzaDsVKrlc1Gj3rrbbe+124lx7XUd9sSEZMaf2uiq1fsW5ud9N0Hoe91NzT5XDR+HSllWNCorHldsdlax557b7K27wS0WVVtclFssys3nZdm2Vr/2hpxvf1uJM/OKn/kHcpfzMvWaZFmy02lZkQ+roo3nyZTLqhcKctfXFX322afON7Gpo6F9bQEAeqcTwe43n/ws7PL7jeC3c3F0CM3MzOjdd9/dcfni4mIfRgMA6IdB/xINhMH4pYuq3rmjyq2bcqQDb1AUxtCl9MZVOffuyk4fbhhq77cZVDO+9Prtpo779T+7ra/8/Hd1bFz7XYesSNv3Tere896vwHgQA+tqJqPSG1dV/dbtzc9Zv7o6pcSZeY1furjjud/+ONQeLqn4//6+nOyiEmfO7Kjurz96JCeTkVsqyTiOv+npoUOSZan8jt+31/zxH8tbW5OdHJdXq8mUy7LGxiTLkiRZkYissTF5lYq80qqsqSk2RAMAtKwTwe7XJdUlzVuWFTfGONt+/+KTn9/uwG2F1uwuFSHZbLbHIwEA9NMgfokGwmRYq+drD5f8oGulqNHzp/Y8NjY9rfKNG6revq3aw6Wmz03NVOtu+NN3H+qvf/9r+kjMUfntG22Nqxf3rVsOEkJ2QxgnKhpZv37df29va8dhqlU52ayc+/dVvXNn13YcWx8H99EjeW98bUd1v1ssyslkVC8UFEkkpJERv8/yzIxGPvIRGddV9e5df1M2Y5R4/nm5H3wgt1RS/fFjWYnEh+0YqlUpFpNljOx0WpHk/ps6AgCwVdvBrjHmkWVZ/4+k/1TSFyX9s43fWZb1H8nfPG1F0r9t97bCbGZmpuHlVOwCwHAalC/RQBgNY/W8s5CRmy8omk7v2VtY8itk7VRKbj4vZyHT9Lmq2WrdDb9+NaN/nn1d9VxOVjzuVzduW+7ezLh6cd+6od0QEk/rdKuR3ar7a4uLckslReJxSZJxHEVTKcVm/PZ6lm3LTialSESmVpNxHCXOnVVt8YG8lRV/QzRjZEWjspNJRSYn/Y3TIpG+vyYBAOHTiYpdSfpFSd8j6b+1LOuHJP2VpJOSflKSK+nzxpjdWjUMBSp2AQAAgmPYqudNtSrjuv6GZE2w4nEZ1/UrCpvQSrWuPyCjv4g/p2+aMZ1aXZUVjap665a/QdWRIy2Nq9v3rRt60e942HS61Uij6v7I2JhquZy8tTUpGlUkkVA0lVJ8bk72oS2TEp6nSDwut1KRt7Ii68QJjTz/vLxyWd5qUcb1ZNkRRQ5NKDI6Kieb7clrcljOdwAwTDoS7BpjlizL+h751bo/Kel7Ja1K+kNJ/8IYc60TtxNmVOwCAIAwG9RAYFiq561EQpZtNx0cGcdRJJmUlUg0dXyr1bobfUZ/5/j364tLCzLr66oXClImIyse37Vyt9G4un3fuqEX/Y6HSaN2HF65LLdYlDxPikRkT/ghaivtOLZX91czC1K97rdeSKcVmZxUbOa5p0NdSYpE/P+iUXnVqrzVoiKjo5v/bdft12RQWn4AADqvUxW7MsYsy6/c/cVOXecgoWIXAACEEYHAYIifnpOdTsnJZhU7fnzPlgXGdeUWCoofO6b46f2f25ardT+8Jf1FbFqZ9DGdXn/Pr3AslVR78KBhsLvbuLp537ohzD2Bg2prOw5vbc1vl1As+mG/MZJlyUokZE9MKDYz01I7jq3V/Stf/Tda/ZM/kWQpPjfXMKSVJHtiwg9pV1b8Xrqut+v1d/s1ScsPABhsHQt2sTcqdgEAQNgQCAyO2NRRJc7My7l/f8dmUNvVcjnZkxNKzM83FSS2XK27ya/a/b+OfZ/++w++LSPJ1Gp+H9JyeUdottu4unnfuiGsPYGDbKMdh1suq37rltxSSaZWkxWP+xuVua689XV5pZK8YlHWoUOKjIy01PogNnVUox/7mMp/+3fy1td3DXUlKTI6KntiQu6jRzKOI8uO7HpsN1+TtPwAgMG3+ycMOmp6elrWkyVnWy0vL6tcLvdhRAAAALvbGghYIyMaPX9e8VOnFJ+dVfzUKY2ePy8rMbIZCFQzmX4PGfsYv3RR8RMn5eaXN3t6bmVcV042Kze/rPiJkxq/+Mq+13nwat3NW9W/S55Q5tlTMo4jGSOvUvGX0Lcwrv3um4zX8n3rljD2BA46K5GQqVRUf/BA9ULhyaqCtOxDhxRJJmUfOiT7SZBeLxRUf/BAplJpufXBRnV4PZ/f+RrbJjo15bdj8Dy5pbWOvN9atb3lx/aJhI2WH3b68GbLD7Sv9nBJa9euqfTmm1q7dk21h0v9HhKAAUbFbo9Eo1FNTU0pl8vt+N2DBw80x8woAAAIkHZ6gA5qP96wa7QZlJ1K+cGh48gtFGRPTmjk7DmlXnu1qcq9g1frbnjSa3fuov7H8iPVHz+WWyyqtrgoU683Pa697ps7ccgPU6uVlu5bt3S6J3Cz77dBfl/GT8/JK/sVufbEhCLJ5I5jrEhEVjIpGSO3WJRXLrfc+qCV6nBvfV3R555TJBaTZDryfmsFLT96j9ZFAPqBYLeHZmdnGwa72WyWYBcABsggf3nGcDhoILD2V3+tyttv86U2wLZvBrXxPEWSScWPHVNifl7jF19p6nlqv1p3g99r9+4L363jb1+Tao4iY2OyIpGWxrXbfbNiMdnj4zr0iR9u+r51U6d6AjcbIg1N2GQkWf6P/Q7TzoWUTRu/dFHVO3dUuXVTjvxz4Nbn0Liuarmc3PyyRj/6UR365D+ScyfT9vutVbT86C1aFwHoF4LdHpqZmdFbb72143L67ALAYBiaL88YeAcJBJxvf1uPv/JleetlvtQG3NbNoNqZhGq/WneDn7L9b/F5/Q8jf6fEkzDMHhtreVyN7tsjx5E9MaFnvud7OjTe9nSiJ3CzIdLISy+q8vY7Ax82OQsZRZJJRZLjMo4jb21NkbExaWsrPGPkra/7FdBjSUXGxg4UYrZa+T524YL0yis9n/Sl5Ufv0MsYQD8R7PbQ7C5/tGWz2R6PBADQaVRqYJC0GgiYel31xUVZ8bhiJ07wpTYkYlNHDxwsda5ad4PRn+uwMkdO6sL585r81KcOfE3bAzR7ZMQP+Rr8rl8rKlqp+hw5e+6p/qvNhkjrf/93Wn/rLVnRqKLT0wP9vtx4PmPPPSdvdVVuqaT648d+24tIRMbz/GPicUVTKUUOHfL78h4wxDxI5Xs777eD6HTLD+yundZFANAugt0e+shHPqLz589rdnZWMzMzmz9/4Ad+oN9DAwC0gUoNDJqtgYBX9itw5XlSJOL3r9y2G3z9gw/kVSqKHznCl9oh0blq3Q1+ZeX/OfXd+qGLB/vbeLdVE+Xv+JiskRE9/ON/Kze/HIgVFe30O242RKpls3IfP5Y9BO/LjXNWZHRUsWOzqi0+kLeyIq9alYyRFY3KTiYVmZxUbOY51R89lmXbbYWYnap875ZOtfzA3uhlDKDfCHZ76Atf+IK+8IUv9HsYAIAOo1IDBxXkQEBRW9VMRrVcTqZWk4yRLMuvgJyYUGxmRvbEhNxSSd7KimRZip08uef18qV2MHS+WneD0Z/rGd1OPKMXW/yXe62aqD18KFOva+Vrb8gaHVV8ZiYQKyoOUvXZbIjklcuS58lzHNmeJ69c3jEhs2EQ3pfbQ8yR55+XVy7LWy3KuJ4sO6LIIX9Syg8x73QsxOx1JW6zOtHyA/ujlzGAfiPYBQCgDVRq4CCC3o+5ln1f9dxDmUpF9fV1f3luJCLjuvLW/Z3nvWJR8bk51R4+3KzktcfH97xevtQOhs5X627wq3Z//c9u6ys//11N/6u9Vk24q0W/z2q9Lq9SUXR8XPbhw7InJiT1f0VFq1WfzYZIbrEoU6v57QZqNXmrxV2D3UF4XzYKMSOjow3v8zCFmO20/EBz6GUMoN8IdgEAaAOVGmhV0Psxb4RkGxV+ruPIikQ2NyIynidTLqteKMh95x0pElFkZET2s0eaun6+1IZb96p1P/Sn7z7UO9kVvTg72dTxe62aqGUXZcYPyYrHZY+Py1tbU+3Bg81gNygrKpqt+mw6RPI8vwVBJCIZI+N6ex4+CO9LQsyd2mn5gebQyxhAvxHsAgDQBio10Iow9GPeCMmi09OKnDwpJ5PZdSMi1euyn31W0VRKVrTJjdb4UrtDUFtyNNK9at2nNVu1u9eqCa9cllcsSp4rKz4qa3RUXj7v917d1pogLCsqmg6RIpHNiRhZliw7sufhg/C+JMRs7CAtP9A8ehkD6DeCXQAA2kClBloR9H7M20Myf3OheMONiKLPPitvfV2xY8dkJ5Oq3rnDl9oWBb0lx3a9qNbd0GzV7l6rJrzVorxq1b/ckqxIRFY8Lq9alVt8ujVBWFZUNBsi2RMTsp6sBLDSaUUOTex6nYP0viTEbCzoG72FGb2MAfQbwS4AAG2gUgPNCkM/5kYhmX1oQvbzEw03IqrlcorYtuzJCdmTE3ypbUHQW3I00qtq3Q3NVO3utWrCuN7mpn8bNloTyNvZmiAMKyqaDZEio6N+m5R43P+5S39dafDel4SYuwvqRm9hRxsQAP1EsAsAQBuo1ECzwtCPea+QrNFGRBtB2MgLL8jU6nypbVIYWnJs18tq3Q3NVO3utWrCsv12BDJm8zLjebKiUb9VwTZhWVHRbIgkOyL7mWdk2bY/+Thk70tCTPQKbUAA9BPBLgAAbaJSA80IQz/mg7YWiZ88qcT8PF9qmxT0lhyNXLn+ft9ud69gd69VE5FDE4okEn6LC+OHusZxZCeTm5unbQjTiopmQ6Sxj32HRl56UZW33+F9CXQZbUAA9AvBbgCsrq6qVqvp8OHD/R4KAOAAqNRAM8LQj7md1iKxqaN8qW1CGFpyNPJTLx/XaqWuuruzhUG3RO2Ifurl43ses9eqicjoqCITE1LElqnXZMplWbGYIpOTO6rPw7aiolGI5K6vyziOokeOKH7ihCZ+7NNKfvd3q/o9Gd6XQA/QBgRAPxDs9tjXv/51feUrX9Hi4qKy2awWFxe1urqqX/iFX9Bv/MZv9Ht4AIADolID+wlDP+Z2W4vwpXZ/YWjJ0cgLMxP6n3/qY327/b3stWoiNjsjKxaVKZfllkqKHjmi2HPPbf7bMK+o2Hi/rf3VX6v4h38g7949GUlyXdUfPtTKv/7Xqtx4W+OXLuqZ//w/430J9AhtQAD0EsFuj2WzWf3O7/zOjssXFxf7MBoAQCcRamEvYenH3InWInyp3V0YWnKEzX6rJpRKSdGoIiMjMq6r+uPHcldXB2JFxfr161r56ld3bMLnra833ISP9yUAAIOFYLfHZmZmGl6ezWZ7PBIAQLcQamE3YejHTGuR7gpDS44w2mvVRGxqStbIiCYnJuUuPx6YFRVh3IQPAAB0FsFuj83uUp1DxS4AAIMvqKFpoyrzZz73WVqLdEEYWnKE1W6rJpYtS5GxMU299NJAragI4yZ8AACgswh2e+y5LT29tsrlcnJdV/Y+vdYAAEC4BakfczWTUemNq/5mXk/GYdm27HRKiTPzGr90UROf/vTABGFB0MmWHIMUUnbS9lUTkbff3vV3YRXWTfgAAEBnEez2WDKZ1OTkpFZWVp663HVdLS0t7Rr8AgCAwRGEfszr16/7lcPbenOaanVHb87k935vT8Y0LNptydFMIE9l5mDr9iZ8W89N7vq6JEv22CgTCAAABAzBbh/Mzs7uCHYlv88uwS4AAMOjX9WD9Obsr3ZacrQSyI9duNDHe4lu6tYmfFsnDWrvZ1V/9Eje+rpkSZHRMUWffVax2RkmEAAACAiC3T6YmZnRu+++u+Ny+uwCAIKOpd+Dgd6c/XeQlhwE8tjQjU34tk4a1B4+lKlUZBxHplaTjJG3ti53dVW1xUUmEAAACAiC3T7YbQO1bDbb45EAANAcln4PDnpzNtaPSYtWW3IQyAdTP147nd6Eb+ukgZUYkWXb8up1RUZHZR0+LMuy5K2vy6tWpUhExvOYQAAAIAAIdvtgZmam4eVU7AIAgoil34Ol2705wyYIkxbNtOQgkA+efr52OrkJn/T0pIG3uipvbU2RREKRZHLzmI3/7a2vy3bTstOHmUAAAKDPCHb7YLeKXYJdAEDQsPR78HSrN2cYhWnSgkA+WILw2ml3E74NWycNEvNTqmWzMrWaIuPjO46NjI2p/vixvJUVxWZnVb29xAQCAAB9RLDbB7tV7NKKAQA6h16wncHS78HTjd6cYRS2SQsC+eAIymunnU34tto6aeCtrfmfm/G4rEhk58GWJSuRkFetyqyvMYEAAECfEez2ARW7ANA9QVhWPShY+j2YOt2bM6zCNmlBIB8cQXrtHGQTvu2emjTwPMmYxqHuE1YkIhkj43pMIAAA0GcEu31AxS4AdEcQlsYOEpZ+D6ZO9+YMozBOWhDIB0MQXzutbsK33VOTBqOjkmX5Qe8ujOfJikZl2RF5lQoTCAAA9BHBbh9MT0/LsiwZY566fHl5WZVKRSMjI30aGQCEV1CWxg4Sln4Prk715gyrME5aEMgHQ5BfO81swtfI1kmDxJEjfquF9XU/wN1euWuMTLUqO5mUNZaUm11kAgEAgD7afY0NuiYajWpqaqrh72jHAAAHs31p7PYv3BtLY7fu4o29bVRxqVZr6njjOLJsu2uVW7WHS1q7dk2lN9/U2rVrqj1c6srtDION3pwjZ8/JVCt+VeHCgpxsVtWFBZVv3JCpVvbtzRlWYZ20GL90UfETJ+Xml+VkszuqKo3ryslm5eaXFT9xcuAC+SAI62tnLxuTBvbkhNyVFdkTE7JiMZlyecex3vq6rHhckclJ/1gmEAAA6CsqdvtkdnZWuVxux+WLi4uaG7AvTwDQbUFcGjsIgrL0m77J3dGJ3pxhFdZ+tZ3aLAsHF9bXzn62VvFbiRFFkkm5KyuSJGt0VJZlyVtfl1etynyVRIEAACAASURBVJ6YkOzIwFb0AwAQJgS7fTIzM6O33nprx+X02QWA1q1ff0vVzIIsy1L90SPZExOKjI42PDYoy6rDIAhLv1vpm9xsBR0+1G5vzrAKyqTFQQxzIB8EYX7t7GX7pIFxXVnRqLxyWaZY9DdUi8VkxePSkxYNCSYQAADoO4LdPpnd5csxrRgAoHkblZylv/hz1e7fl/E8uaurshIJ2RMTis3M+JVF24RhaWxQ9LMXa6t9k90f/ZTsycmO3f4wOWhvzrAKwqRFO4Y1kA+CsL929rJ90qD2flb1R4/kra9LlqXI6Kiizz6r2OwsEwgAAAQEwW6fzMzMNLycYBcAmrO1krOey/k9D42Rqdf95aKlkrxiUfG5OUWPHHnq34ZlaWwQ9HPp9/a+ydtt9E12JDn37qr2fpZgtwXDHgoOwgZywxbIB8UgvHZ202jSwF1fl2TJHhsdynMFAABBRrDbJ7tV7NKKAQD2t72Sc+RjH1P13XdVX16WPT4uY4xMuax6oSBlMrLi8c3K3TAtjQ2Kfiz9PkjfZLeQV/3xstauXRvasLIZ9Cz20a8WBzUMrx0mDQAACAeC3T7ZrWL3gw8+6PFIACB8GlVyRiYmZJVK8tbX/WrcZFKS5JZKqj14sBnshm1pbFD0eum3s5CRmy8omk7v2cNS8it3rUTCXzJ8/bqW33tvaMPK/bTSs3jswoV+D7fr6FeLg+K1AwAAgoBgt09efPFF/eqv/qpmZmY0Ozu7+XOSJaQAsKfdKjljszPyikW/SldSZGxM1uiovHxe3sqK3FJJ7spKKJfGBkmvqrhMteq312hiQ7T6o0eqLy35m/w8acUxzGHlblrtWWynUkMRStGvFgfFawcAAPQbwW6fHDt2TL/8y7/c72EAQOjsVslpH5pQfG5OymTklkqqP37s99A1RvV8Xt7f/71iz02HemnsMLESCVm2ve8Gd26xKCeTkVcqSVZE9mRK8VOnNn8/rGFlI632LC5dfXOoHqtBWHpOwNgfg/DaAQAA4USwCwAIlb0qOaNHjshKxFVbfCBvZUVetSpTq8mKRBQ/cULjP/iDLI0NifjpOdnplJxsVrHjx3dtx1BbXJRbKknGKJKI79gQb9jDyg0H6VlcvX1btYdLBFYhQN9kAACA4USwC6BpVAIhCPar5LQPTch+fkJeuSxvtShn8YEio6NK/fRPa/JT/7jHo8VBxaaOKnFmXs79+6rlcg0rTL1yWW6xKG99XdbYmKx4Qla08Z82wx5Wttqz2E6l5ObzchYyXXus+EzpDPomAwAADC+CXQD7ohIIQdJsJWdkdFRWPC5lF5WYmyPQCKHxSxdVvXNHlVs35cgPZ7c+326hIHdlRZIUPXRIkfHkrtfVq7AyqFrpWSxJVjwu47r7tsI4CD5TOoe+yQAAAMONYBfAnqgEQtA0U8m5oZbLyZ6cUGJ+fuiCvEGQmJtT6rVX/XPQvbsq37ghO5XyQ0fHUS2blVxXdjKp+NycrFh8z+vrZlgZdM32LN5gHEeRZHJHa4t28ZnSWfRNBgAAGG4EuwB2RSUQgmq/Sk7juqrlcnLzyxo5e07jF1/p32CHUCeX2I9duCA7lVLp6puq3n5vs8IzkkwqMjen2oMHioyNKXrkyL7X1a2wMgyarXSX/PePWygofuyY4qc7d07nM6Wz6JsMAAAAgl0Au6ISCEG1XyWnWyjInpzQyP/P3v3GNpLnd37/FFn8r2WTkshukd2abnkkT2N2B6uxEcPGrafHRhYIDAR2Zu7hJRvnDMMIsDDg2AEOcGAECHBPgvgQwBvj1vAlF/jRTJ4YDhLAt9PjP+uFDzNyenZ3ZqUdaVs9pNQU2WTXiCJZZLHyQCtO62+rJZJVRb1fT2a3VC19u8Uqsj71/X3rlbvKvP0Wr8sxGdUS+9jCgmILC8cC49CX0qr/n/9ere//YH/MwBlGFVYGhR863XlPGS4/zk0GAADAeBHsAjgRnUDwu7M6OaM3byq2uKipe28MPRjigU8nG8cS+8j1/LF/671nwkq99NKpf5axHN52uvOeMnx+mpsMAAAAbxDsesx1XVWrVZXLZZVKJZVKJUnSb/3Wb3lcGa46OoEQBKd1co4ibOWBT6fzcon9s2Gls7urcCp56OuM5fiCl53uvKcMn1/mJgMAAMA7BLse+slPfqKf/dmflW3bh7YXi0WCXXiOTiAEyUmdnMPEA5/O5uUS+2fDSjk99apVdTY2GMtxCq863XlPGT4/zE0GAACAtwh2PZTP54+FupK0vb0tx3EUfk5HCzBKdAIB+/z2wCe/jYLwwxL7g7Cy9I//UU6jrnAqNZawMqjG2el+gPeU4fPD3GQAAAB4i2DXQ8lkUplMRo1G49B2x3FUqVQ0NzfnUWUAnUDAAb888MmvoyD8ssQ+trCgeLOp/t6epr/6Vd8E33426k73Z/GeMhpezk0GAACA9wh2PVYoFI4Fu5JULpcJduEpOoEAf3SjSv4eBeG3JfahZFKpr3xlJN8bF8d7ymh4OTcZAAAA3iPY9VixWNQPf/jDY9tLpZJ+7ud+zoOKgC/QCYSrzg/dqH4bBXEUS+xxXlfhPcWLUSlezU0GAACA9wh2PVYoFE7cXi6Xx1wJcBydQLjq/NCN6pdREKdhiT3Oa5LfU7weleLF3GQAAAB4j2DXY8VTliKWSqUxVwKcjE4gXGVed6P6ZRTEmT+XJfZ4AZP4nuKnUSnjnJsMAAAA7xHseoyOXQQBnUC4qrzuRvXDKIjzuApL7DE8k/Se4vdRKQAAAJhsBLseOy3YpWMXfkQnEK4ar7tR/TAK4jwmeYk9RmcS3lP8PioFAAAAk41g12OnjWKgYxcA/MHLblSvR0G8iElcYg+cJQijUgAAADDZCHY9RscuAPibl92oXo+CeFGTtMQeeJ6gjEoBAADA5CLY9diNGzdkGIZc1z20/cmTJ2q324rH4x5VBgA44FU3qtejIC5qEpbYA88TlFEpAAAAmFwEux4zTVPXr1/X9vb2sa+Vy2UtsGQVAHzBq25UHkwG+FOQRqUAAABgMhHs+kCxWCTYBYCAGHc3Kg8mA/wpaKNSAAAAMHkIdn2gUCjogw8+OLadObsAAIkHkwF+FNRRKQAAAJgcBLs+UDzlQqBcLo+5EgCAX/FgMsB/GJUCAAAALxHs+kChUDhxOx27AICjeDAZ4B+MSgEAAICXCHZ9gI5dAACAYGJUCgAAALxCsOsDdOwCAAAEF6NSAAAA4AWCXR84LdilYxcAACA4GJUCAACAcSLY9YHTRjGUSiW5rivDMMZcEQAAADAcdDIDAACMBsGuD0xPTysWi6nT6SibzapYLKpQKKhYLKrb7SoajXpdInyOCybAWxyDAHBcZ31du+/dV+fHa4PZw0Y4rHA2o9jLi5p68x6zhwEAAC6BYNcHDMPQj370I+VyOSWTSa/LQYBwwQR4i2MQAE629+GHarzzruyHD+VYlsxsVopE5HY6sksl2Y8eqfPpp8q8/ZaSr7/udbkAAACBRLDrEy+99JLXJSBguGACvMUxCAAn66yvq/HOu2p/8rHC2Wklbt+WEQ4Pvh65dUvd7W21P/lYjXfeVTiT4SYYAADABRDsAgHEBRPgLY5BADjd7nv3ZW8+VDg7regJz5IwwmFFi0XZkuzNh9q9/z7nSAAAgAsIeV0AgBd39ILp2UBJ+uKCKZydHlwwARgejkEAOFn3cWV/PM1TS5EbN87cN3Ljhpynljpra+o+roypQgAAgMlBsAsEDBdMgLc4BgHgdPbGupx6Q2Y2e+ym11FGOKxwJiOnXpe9sT6mCgEAACYHwS4QMFwwAd7iGASA07mdjlzHkSKRc+1vRKNyHUdupzPiygAAACYPwS4QMFwwAd7iGASA0xmx2P5Nr273XPu7ti0jHJYRi424MgAAgMnDw9OAgDm4YDpvSOTatkKpFBdMV0T3cUX2xrrcTkdGLKbonQVFrue9LmuicAwCwOmidxYUzmZkl0qK3Lp15soG13HkNBqK3ryp6B0engYAAPCiCHaBgOGCCSfprK9r9737+7Nf6w25jrM/BiCbUezlRU29eY8njg8JxyAAnC5yPa/Yy4uyHz1Sd3tb0WLx1H2729sKX0srtrjITUgAAIALINj1kb/6q7/SxsaGSqWSyuWyyuWySqWSvvOd7+jGcx7Qg6uDCyYctffhh2q8867shw/lWJbMbFaKROR2OrJLJdmPHqnz6afKvP2Wkq+/7nW5gccxCABnm3rznjqffqr2Jx/L1v6DJJ+9CeY6jrrb23LqTxR/5a6m7r3hXbEAAAABRrDrI3/wB3+gH/7wh8e2f/bZZwS7OIQLJhzorK+r8c67an/yscLZaSVu3z70WojcuqXu9rban3ysxjvvKpzJ0Lk7BByDAHC62MKCMm+/tX/TcfOhWg8eKJzJ7M8ct205jYbC19KKv3JXmbff4n0JAADgggh2faRQKJwY7JbLZQ+qgZ9xwYQDu+/dl735UOHs9Imdo0Y4rGixKFuSvflQu/ffn5jXg5fzhDkGMcmY1Y1hSL7+usKZjHbvv6/O2upgTFAolVL05k3FFhc1de8Nzo8AAACXQLDrI8VTlvOWSqUxV4Ig4IIJ3ceV/Zm6Ty0lXrt95r6RGzfUevBAnbU1dR9XAh3S+GWeMMcgJo1fji1MjtjCgmILC9wsAAAAGBGCXR8pFAonbqdjF6fhgulqszfW5dQbMrPZMx/gJe137oYzGTn1uuyN9cC+Pvw2T5hjEJPCb8cWJkvkep5zIgAAwAgQ7PoIHbu4KC6Yria305HrOFIkcq79jWhUruPI7XRGXNlo+HmeMMcggszPxxYAAACA04W8LgBfoGMXwIswYrH98KXbPdf+rm3LCIdlxGIjrmw0js4TPtqlfDBPOJydHswTBvB8HFsAAABAMBHs+ggduwBeRPTOgsLZjHr1+n7n7hlcx9l/oFc2q+id4HXaPTtPOHLjxpn7Rm7ckPPUGswTBnA6ji0AAAAguAh2fYSOXQAvInI9r9jLiwpfS6u7vX3mvt3tbYWvpRVbXAzkyIDLzBMGcDqOLQAAACC4CHZ95MaNGzIM49j2J0+eqNVqeVARAL+bevOeovMvyak/kV0qHevcdR1Hdqkkp/5E0fmXNHXvDY8qvZyrNk8YGBeOLQAAACC4eHiaj5imqevXr2v7hM67ra0tLfCgEgBHxBYWlHn7rf2n2W8+VOvBA4Uzmf3wxbb3xy9cSyv+yl1l3n5rLA886j6uyN5Yl9vpyIjFFL2zcOku4YN5wucNk1zbViiVCuw8YWBcOLYAAACA4CLY9ZlisXhisFsqlQh2A2gUARdwVPL11xXOZLR7/3111lbl1BtyHUehVErRmzcVW1zU1L03Rh7qdtbXtfve/f15nT+twQiHFc5mFHt5UVNv3rtwDQfzhO1SSZFbt85cMn4wTzh682Yg5wkD48SxBQAAAAQXwa7PFAoFffDBB8e2M2c3WEYZcAEniS0sKLaw4NnNhL0PP9zvGn74UI5lycxmpUhEbqcju1SS/eiROp9+qszbbyn5+usv/P0P5gnbjx6pu72t6CkPm5SCP08YGCeOLQAAACC4CHZ9pnjKBRXBbnCMOuACzhK5nh974NJZX1fjnXfV/uRjhbPTSty+fajrL3Lrlrrb22p/8rEa77yrcCZzoRsbU2/eU+fTT9X+5GPZkiI3bhz6Oa7jqLu9Laf+RPFX7gZ2njAwbhxbAAAAQDAR7PpMoVA4cXupVBpzJbiIcQVcgJ/svndf9uZDhbPTJ3b7GeGwosWibEn25kPt3n//Qq97P84TBiYBxxYAAAAQTAS7PkPHbrCNK+AC/KL7uLI/cuSppcRrt8/cN3LjhloPHqiztqbu48qFOov9Mk8YmDQcWwAAAEDwEOz6DB27wTXugAvwA3tjXU69ITObPfOhS9L+jY1wJiOnXpe9sX7h173X84SBScWxBQAAAATLyIJdwzD+haT/46f/97dc1/32qH7WJKFjN7i8CLgAr7mdjlzHkSKRc+1vRKNyHUdup3Ppn+3FPGHgKuDYAgAAAIJhJMGuYRi3JP2vknYlTY3iZ0yqszp2XdeVYRhjrgjn5WXABXjFiMVkhMPnfh27tq1QKiUjFhtxZQCAq+zZzvOubSucTntdEgAAwNANPdg19pPHP5dUk/R/Sfrvhv0zJtn09LRisZg6R0KSVqulp0+fKpPJeFQZnoeAC1dR9M6CwtmM7FJJkVu3zuxWdx1HTqOh6M2bit5hTicAYPg66+vafe/+/nisn86Kbn/5VYViMdW+/wNNvXmPWdEAAGBihEbwPb8p6Vck/deSmiP4/hPNMAzm7AbUQcDVq9f3O3fPcBBwhbNZAi4EWuR6XrGXFxW+llZ3e/vMfbvb2wpfSyu2uMgybwDA0O19+KFq3/4zff6d76j1/R+ov7cnt9+X2+2pV6vp8/e+o9q3/0x7H37odakAAABDMdRg1zCMu5L+taR/47ru3wzze18lzNkNJgIuXFVTb95TdP4lOfUnskulYzc2XMeRXSrJqT9RdP4lTd1749DXu48ran7ve9p9/301v/c9dR9Xxlk+AGACdNbX1XjnXbU/+VhGPK7Ea68pevu2osWiwum0zNlZGbG42p98rMY776qzvu51yQAAAJc2tFEMhmGYkv69pE1J/+oCf/6DU770Sq/X00cffXSZ8gLllVdekWmayufzyufzyuVyyufzSiQSV+rfIYicn11Su9tVr/5ERiyucCopGc/cP3H7cpp7chNxmdlpNZYWVeZ3eiHValWSOCZ8overv6LO/Lyczy25tr0/YiQUlvr7c6SNV35W4S+lFVt8WbVmU/roIzlPn6r72WdyGg31Ox2p70ohQ6F/+ieFMxlFbt5U+No1r/9qCBDOC8DV1f7BD2RnM9I/+5rCU4cf8fH5wf//hV+Qs7srOT2V/vE/Kt5kcSFwlfG5AcBR4zovtFqtoX2vYc7Y/R8kLUv6Z67rDq/CK+ib3/ym1yXggsLXrim2+LK09mM5n1vqVavHA65oVGZ2WrHFlwmtMDHMfF5GLKbuZyU5jfoXQW0kovDUlMKZrCI3i4PXfK9SUeenx8l+EByXQiGp66i3uyvn88/lNJ4qtviyzDxd7QCA0/X39uQ0GnJtW+bs2Q9JC6eS6lWr++9Ve3sKJZNjqhIAAGD4hhLsGobxn2i/S/d/dl33Hy7yPVzX/blTvvcHpmm+/pWvfOUyJQJj1blzR7v331dnbVXOo8/kOo6McFjhbFaxxYKm7r3Bgzsu6eAOGucG/3n2SeRGLKbonYVDI0c66+uq/YfvqP3JxwpnpxW5cUNGxx583XUcddc35NSfKL65qZl/+d9wvOBcOC8AV1Pze9/Tk3/6/9Tf21P0mfeTAw9v3pQkvfTZZ5KkzsaGwqmUpr/6VaU4XwBXFp8bABw1rvNCIpEY2ve6dLD7zAiGVUl/eOmKgAkQW1hQbGHhuQHXqHn983E1Ra7nz3yd7b53X/bmQ4Wz04qeMFPcCIcVLRZlS7I3H2r3/vsEuwCAU7mdzv5890jkXPsb0ahcZ38lFQAAQJANo2N3StLST/932zCMk/b5t4Zh/FvtP1Ttd4fwM4FAeF7ANSqd9XXtvndfnR+vyak3nukYzij28qKm3rxHUAZPdB9X9l+XTy0lXrt95r6RGzfUevBAnbU1dR9XuCkBADiREYvJCIfPHdS6tq1QKrU/LgsAACDAhhHsdiT92Slfe137c3f/TtKPJF1oTAOA89v78EM13nlX9sOHcixLZjYrRSJyOx3ZpZLsR4/U+fRTZd5+S8nXX/e6XFwx9sa6nHpDZjYrIxw+c18jHFY4k5FTr8veWCfYBQCcKHpnQeFsRnappMitW2e+v7iOI6fRUPTmTUXvcJMbAAAE26WD3Z8+KO1fnvQ1wzD+SPvB7v/uuu63L/uzAJyts76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      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 306,
       "width": 699
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(*X1.T, alpha=0.6, c=\"tab:red\")\n",
    "plt.scatter(*X2.T, alpha=0.6, c=\"tab:gray\")\n",
    "plt.scatter(*m1, marker=\"^\", s=200, c=\"tab:blue\")\n",
    "plt.scatter(*m2, marker=\"^\", s=200, c=\"tab:blue\")\n",
    "plt.plot(projected_space, projected_line, linestyle=\"dashed\", c=\"black\", linewidth=3)\n",
    "plt.xlim(0, 5.1)\n",
    "plt.ylim(-1.8, 8)\n",
    "plt.grid(alpha=0.7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One drawback of the optimization problem above is that\n",
    "> Two classes that are well separated in the original space may have significant overlap when projected onto the line joining their means"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fisher's approach to project and classify"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
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